In Cuba there are banknotes with values of 3, 10 and 20 pesos. Using only these banknotes, what is the largest amount that can not be formed?

1 Answer
Apr 4, 2017

#17#

Explanation:

What an intriguing question!

Note that the first 10 multiples of 3 end on every possible digit from 0 to 9.

#3," "6," "9," "12," "15," "18," "21," "24," "27," "30#

Arranged so the units are in order from #0# to #9:#

#30," "21," "12," "3," "24," "15," "6," "27," "18," "9#

Every number from #20# upwards can be written either as a multiple of #3 or 10#, or as the sum of a multiple of #10# and a multiple of#3#.

#20 = 10+10#
#21 = 7 xx3#
#22 = 10+12 = 10 +4 xx3#
#23 = 10+3#
#25 = 10+15 = 10+5xx3#
#26 = 20+2xx3#
#28 = 10 +18 = 10 +6xx3#
#29 = 10+3xx3#
#31 = 10 +21 = 10 +7xx3#
#32 = 20+12 = 20+4xx3# etc.....

What about the numbers less than 20 that cannot be formed with # 3 and 10?#

#19 = 10+9 = 10+3xx3#
#18 = 6xx3#
#17 = ???????????????#